Salt is very destructive on natural stone over time. You could seal the stone with a powerful sealer and then plan on redoing that every year to prevent the erosion. Pebble Tec is a very legitimate product. It's at the high end of plasters, but it is probably the best finish around.

Flagstone is a bit of a generic word. Many different stones are split and cut into random like pieces that are referred to as flagstone. Stone is not created equal, some are very soft and pourous, and others very hard. I have had many stone features, and water features built with flagstone in salt pools with no problems. Stick to a harder stone, or a Quartzite.

There has been a big debate over salt destruction of stone for a long time.
I had for almost a year, a piece of flagstone in a jar of water, and one in a jar of salt water, both stayed identical.
Many will say it is ok under water but it is the build up of salt with the wet and dry. Well I have seen flagstone fall apart in a non salt pool due to dogs (labs) getting in and out 100 times a day in the same spot, and the stone getting wet/dry.
The only stone that I wont recommend around a salt pool is Cantera stone, very soft and sponge like.

You could always dip the stone or otherwise coat all 6 sides in an impregnating sealer like Dry Treat. It is also a consolidator so it is supposed to make the surface of the stone stronger. Then you are supposed to let it cure for 14 days and then can use special mortar to fix sealed stone to beam of pool. That's about as anal as you can get with stone but it should alleviate all worries.

In general, if you can scratch it with a nail and the line produced is white, don't use it. If the line produced is gray or non-existent, it's ok to use.

Salt is not corrosive but electrolysis is, and chlorine can be. Pure water is an insulator and will not conduct electricity. Adding minerals and impurities changes this though. Salt is a mineral. Adding it to a pool can allow tiny electrical currents to cause corrosion, such as rust, to form. Modern constructions methods, such as the use of a bonding grid, generally prevent this.

Porous stone can absorb salted water. Salt doesn't evaporate. As the water evaporates, salt crystals can be left behind. While not a particularly hard mineral, it does have different expansion and contraction rates than the stone. This can potentially cause a very slow erosion process but I have never knowingly seen it as weathering from rain and temperature changes typically have much more of an effect.

I am not a fan of using stone that should be sealed to begin with. They can change the color and or texture. Reapplications often don't get done.